Stress Test = Guesswork

Well, we’ve heard a ton about stress tests recently. Want some details on what a stress test entails? The Journal has some details about the tests here. Now, as much as I think GDP and unemployment are fine things to project forward for economists, let’s walk through the way one would use this to actually price an asset. Let’s start with something simple, like a 10-year treasury note (note that treasury bond specifically refers to bonds with a 30-year maturity). Here are all the components one would need to stress test the value of a treasury note.

1. Characteristics of the note itself: coupon, payment dates, maturity dates, etc.
2. What the yield curve would look like at the date you’re pricing the note.

Why would one need to know the shape of the yield curve (term structure of rates)? This is important, in order to “PV” the bond’s cashflows most accurately, one would discount each cashflow by it’s risk–the simplest proxy is to discount each cash flow by the rate of interest one would need to pay to issue a bond maturing on that date. For the government, this rate of interest is the point on the treasury yield curve (actually, the par zero curve) with the same maturity date. An example would be, if I were going to price a cash payment I will receive in two years, and the government can currently issue two-year debt at 5%, I should discount my cash payment (also from the government, since it’s a treasury note) at 5%. Treasuries are the simplest of all instruments to value.

Here’s an example, form the link above, of what a treasury yield curve might look like:

Now, it is completely and totally guesswork to figure out, given unemployment and GDP figures, what the yield curve will look like at any date in the future. Indeed, one can plug these projections into a model and it can come up with a statistical guess… But the only thing we know for sure about that guess is that it won’t be accurate, although it might be close. However, things like inflation will drive the longer end of the yield curve and monetary policy will drive the shorter end, so these certainly aren’t directly taken from the stress test parameters, but would need to be a guess based on those parameters. This is a large source of uncertainty in pricing even these instruments in the stress test.

Next, let’s examine a corporate bond. What would we need for a corporate bond?

1. Characteristics of the bond: coupon, payment dates, maturity dates, special features (coupon steps, sinking funds, call schedules, etc.), where in the capital structure this bond sits, etc.
2. What the yield curve would look like at the date you’re pricing the bond.
3. The spreads that the corporation’s debt will carry at the date you’re pricing the bond.

Oh no. We already saw the issues with #2, but now we have #3. What will this corporations credit spread (interest/yield required in excess of the risk free rate) at the time of pricing? Will the corporations debt, which could trade at a spread of anywhere from 5 to 1500 basis points, be lower? higher? Will the corporations spread curve be flatter? steeper?

Here is a good illustration of what I’m referring to (from the same source as the figure above:

There, the spread is the difference between the purple line and the black line. As you can see, it’s different for different maturity corporate bonds (which makes sense, because if a company defaults in year two, it’ll also default on it’s three year debt... but the companies’ two year debt might never default, but the company might default during it’s third year, creating more risk for three year bonds issued by that company than two year bonds). It shouldn't be a surprise, after our exercise above, to learn that the best way to compute the price of a corporate bond is to discount each cashflow by its risk (in my example above, regardless of whether the company defaults in year two or year three, the interest payments from both the three year and two year debt that are paid in one year have the same risk).

Well, how does one predict the structure of credit spreads in the future? Here’s a hint: models. Interest rates, however, are an input to this model, since the cost of a firm’s borrowing is an important input to figuring out a corporation’s cashflow and, by extension, creditworthiness. So now we have not only a flawed interest rate projection, but we have a projection of corporate risk that, in addition to being flawed itself, takes our other flawed projections as an input! Understanding model error yet? Oh, and yes unemployment and the health of the economy will be inputs to the model that spits out our guess for credit spreads in the future as well.

Next stop on the crazy train, mortgage products! What does one need to project prices for mortgage products?

1. Characteristics of the bond: coupon, payment dates, maturity dates, structure of the underlying securitization (how does cash get assigned in the event of a default, prepayment, etc.), etc.
2. What the yield curve would look like at the date you’re pricing the bond.
3. The spreads that the debt will carry at the date you’re pricing the bond.
4. What prepayments will have occurred by the date you’re pricing the bond and what prepayments will occur in the future, including when each will occur.
5. What defaults will have occurred by the date you’re pricing the bond and what defaults will occur in the future, including when each will occur.

Oh crap. We’ve covered #1-3. But, look at #4 and #5 … To price a mortgage bond, one needs to be able to project out, over the life of the bond, prepayments and defaults. Each is driven bydifferent variables and each happens in different timeframes. Guess how each projection is arrived at? Models! What are the inputs to these models? Well, interest rates (ones ability to refinance depends on where rates are at the time) over a long period of time (keep in mind that you need rates over time, having rates at 5% in three years is completely different if rates where 1% or 15% for the three years before). General economic health, including regional (or more local) unemployment rates (if the south has a spike in unemployment, but the rest of the country sees a slight decrease, you’ll likely see defaults increase). And a myrid of other variables can be tossed in for good measure. So now we have two more models, driven by our flawed interest rate projections, flawed credit projections (ones ability to refinance is driven by their mortgage rate, which is some benchmark interest rate [treasuries here] plus some spread, from #3), and the unemployment and GDP projections.

I will, at this point, decline to talk about pricing C.D.O.s … Just understand, however, that C.D.O.s are portfolios of corporate and mortgage bonds, so they are a full extra order of magnitude more complex. Is it clear, now, why these stress tests, as they seem to be defined, aren’t all that specific, and potentially not all that useful?

Comments

[PaperGains:]

It's a shame the government is having to do what banks say they did all along. When big banks build risk models, they build them to say what they want them to say. The best decisions are based on both quantitative and qualitative analysis.

In my view, the government should set a benchmark for model inputs, parameters, and type of output. I know they say they do in some areas, but they give banks too much room to wiggle.

papergains

Mar 16 01:18 PM

[Moon Kil Woong:]

Thanks for the article. I hope people read it. You could also say stress test = a con, a lie, a deception. It is shoddy rationalization build after the fact to jusify continued government support to failing institutions.

If the financial institutions were solvent and stable then we wouldn't even be having this discussion. So by default in some sense of the word the government has already admitted these financial institutions would fail a stress test and need bailouts even under existing conditions.

I suppose if the outcome determines a few banks/financial and insurance intitutions aren't solvent enough to justify more government funds it is better than now where we support all of the too big to fail institutions no matter how reckless they are.

But I'm not clapping. John Thain points out one fact quite succintly, if one can predict all the variables accurately then there is no more risk which is a lie. The whole premise of the exercise and why financial institutions are in troble is that the variables are great and consequently so too is the risk. To deny that is to deny simple facts.

It's like telling a kid who doesn't want to figure out a coin flip probability equation that you will tell him the outcome and he can figure out how many coins were not heads. You would have turned the scenario into a simple subtraction equation. Similarly, they are also completely missing the point. So much so, telling them different would be useless because if they understood they wouldn't make such a silly proposal in the first place.

Mar 16 01:21 PM

[NITAFL:]

When I was in banking ten years ago, "Treasury Bond" referred to Treasury debt that had an initial maturity date of ten years or longer, not 30 years.

Treasury bonds that were issued to mature in 30 years were referred to as "The Long Bond."

Has the terminology changed?

Mar 16 02:09 PM

[CautiousInv...:]

A well written and informative article.

And while there are many issues in imposing the stress tests, there are two I would like to point out.

The ability to take two different macro economic environments, and draw asset specific inferences from these larger economic assumptions. And related to this is the likelihood of this being done in the same way by 19 different institutions.

And once we have drawn asset specific inferences, what is the likelihood each of the 19 institutions will both classify the assets similarly......liquid market or no liquid market.....and what is the likelihood each institution will use the same or similar discounting models to reach a hold to maturity value.

From the Treasury's perspective and the perspective of policy development, these are large issues because after the stress test Treasury will neither have a uniform view of the consequences of an adverse scenario, nor a handle on the asset baskets and their valuation under either scenario.

Mar 16 02:33 PM